Question

"(1+CotA+cosecA) (1+cotA-cosecA)= (cotA/2-tanA/2)" prove this.​

Answer 1

Using this (a-b)(a+b) = a² - b².Where a=1+cota and b=coseca.-> (1+cota)² - cosec²a-> 1 + cot²a + 2cota - cosec²aIdentity: cosec²x - cot²x = 1 using it.-> 1 + (-1) + 2cota-> 2 cot a-> 2 cos a / sin aUsing half angle formula for cosine and sine.:-> [2 (cos² a/2 - sin²a/2)] / (2 sin a/2 cos a/2)-> (cos² a/2 - sin²a/2) / (sin a/2 cos a/2)Divide numerator and denominator.-> cos² a/2 / (sin a/2 cos a/2) - sin²a/2 / (sin a/2 cos a/2)-> cot a/2 - tan a/2..hence proved